Wang Bing, Sun Zhiwen, Han Yuexing
School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China.
Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai 200444, China.
Entropy (Basel). 2020 Nov 12;22(11):1287. doi: 10.3390/e22111287.
As network data increases, it is more common than ever for researchers to analyze a set of networks rather than a single network and measure the difference between networks by developing a number of network comparison methods. Network comparison is able to quantify dissimilarity between networks by comparing the structural topological difference of networks. Here, we propose a kind of measures for network comparison based on the shortest path distribution combined with node centrality, capturing the global topological difference with local features. Based on the characterized path distributions, we define and compare network distance between networks to measure how dissimilar the two networks are, and the network entropy to characterize a typical network system. We find that the network distance is able to discriminate networks generated by different models. Combining more information on end nodes along a path can further amplify the dissimilarity of networks. The network entropy is able to detect tipping points in the evolution of synthetic networks. Extensive numerical simulations reveal the effectivity of the proposed measure in network reduction of multilayer networks, and identification of typical system states in temporal networks as well.
随着网络数据的增加，研究人员分析一组网络而非单个网络，并通过开发多种网络比较方法来测量网络之间的差异，这比以往任何时候都更加普遍。网络比较能够通过比较网络的结构拓扑差异来量化网络之间的不相似性。在此，我们提出了一种基于最短路径分布并结合节点中心性的网络比较度量方法，用局部特征来捕捉全局拓扑差异。基于所表征的路径分布，我们定义并比较网络之间的网络距离，以衡量两个网络的差异程度，并定义网络熵来表征一个典型的网络系统。我们发现网络距离能够区分由不同模型生成的网络。沿着路径组合更多关于端点节点的信息可以进一步放大网络的差异。网络熵能够检测合成网络演化中的临界点。大量数值模拟揭示了所提出的度量方法在多层网络的网络约简以及识别时间网络中的典型系统状态方面的有效性。
